Radial basis interpolation on homogeneous manifolds: convergence rates

Abstract

Pointwise error estimates for approximation on compact homogeneous manifolds using radial kernels are presented. For a ${\mathcal C}^{2r}$ positive definite kernel κ the pointwise error at x for interpolation by translates of κ goes to 0 like ρ r , where ρ is the density of the interpolating set on a fixed neighbourhood of x. Tangent space techniques are used to lift the problem from the manifold to Euclidean space, where methods for proving such error estimates are well established.